Construction union officials should be barred from positions with influence over major infrastructure projects, the coalition urges in a bid to stamp out alleged crimes and outlaw bikie activity.
The union's Victorian and South Australian branches have been placed into administration after allegations of criminal behaviour and links with bikie gangs, with the claims to be independently investigated.
The allegations have prompted coalition calls for CFMEU officials to be axed from advisory roles in government projects, such as the Housing Australia Future Fund.
Three CFMEU officials were on the board of its affiliate superannuation organisation Cbus that committed $500 million to the fund, Liberal senator Andrew Bragg said.
The super fund should have no involvement with the housing program while the allegations were probed, the senator said.
"It is very murky. We cannot have bikies and underworld figures involved in a government agency like the HAFF," he said.
"I call on Housing Minister Julie Collins to show leadership and maintain integrity over taxpayer funds by banning Cbus from any involvement in the HAFF."
Queensland Labor Premier Steven Miles has declared he won't meet with CFMEU officials until standover tactics were stamped out in his state.
Victorian Premier Jacinta Allen conceded the response to allegations of violence by union representatives in her state was too slow.
The crime link allegations have rocked South Australia.
"We can't pretend it's just something that affects Victorians," Acting Premier Susan Close said.
While there was no evidence of nefarious activity in South Australia, the police commissioner was asked to investigate "so we can be assured that has not come over the border", Dr Close said.
The federal government has not ruled out deregistering the CFMEU, but the union's national secretary warned that would be a backward step.
"Deregistration would be a disaster for workers," Zach Smith told ABC radio.
"This is a dangerous, precarious industry and the last thing you want is workers to be left vulnerable and without representation, without protection in an industry like ours."
The Albanese government needed to sever ties with the CFMEU, opposition spokeswoman Michaelia Cash said.
"All Australians are seeing the consequences of Labor bowing down to a lawless union, blindly following the demands of CFMEU thugs," she said.
One federal Labor MP, speaking on the condition of anonymity because they were not authorised to discuss internal party matters, questioned whether the ALP should cut ties completely.
Emphasising people's fears about speaking out against the union, the MP said they wanted to remain anonymous because they did not "want to wake up next to a horse's head".
The ordeal was a distraction and the labour movement was "sick and tired of the CFMEU", they said.
"About f***ing time. They're not very nice people," they said.
They accused the national executive of turning a blind eye and raised concerns CFMEU members could still play a role in Labor processes.
Cabinet minister Bill Shorten said the culture in parts of the CFMEU was unhealthy.
"The clear evidence emerging is there's a level of penetration in some parts of the construction sector by organised crime which is far beyond acceptable," he said.
